**Question:**

*True/False?*

There exists a continuous surjective map from the complex plane onto the non-zero reals.

*Hint:*

Search for topological invariants.

**Discussion:**

Under a continuous function, connected set must go to connected set. The complex plane \(\mathbb{C}\) is connected.

It’s image must be connected.

\(\mathbb{R}-0\) is not connected.

So the statement is *False*.

*Related*